Tracking of state of charge in energy storage devices or energy storage assets can be a significant challenge. The most common method of state of charge estimation involves the measurement of current and its integration. However, integration of bias errors in the current measurement often results in large errors in the state of charge estimate. Aliasing errors are an example of such bias errors and are one of the most common of such errors.
Thus, performing state of charge measurements over long periods of time may become a significant challenge and, for example, may require periodic corrections which utilize the characteristics of the energy storage device. The feasibility of such corrections is highly dependent on the specific cell chemistry as well as the particular application of interest. Such corrections may also be disruptive to the operation of the storage device and are generally not desired.
In general, bias errors introduced by aliasing can be minimized using a sampling system that involves an analog anti-aliasing filter followed by sampling at the appropriate rate, for example, as guided by Nyquist rule. An example of such a scheme is shown in FIG. 1. In this approach, the sample frequency, ω1, is chosen to be significantly larger (typically, for example, five to ten times larger) than the cut-off of the anti-aliasing filter to avoid aliasing.
However, the sampling scheme illustrated in FIG. 1 requires the design and implementation of an analog filter based on assumptions of the spectral content of the input signal to be sampled as well as the sample rate implemented.
As such, changes in the assumptions or observed characteristics related to the spectral content of the sampled signal or the sample rate require corresponding changes in the analog filter. Such changes to the analog filter are often expensive and time consuming. Therefore, the sampling scheme illustrated in FIG. 1 is not easily adaptable to varying circumstances or applications.
One alternative to an application-specific anti-aliasing filter is the use of a configuration with a fixed analog anti-aliasing filter design; an appropriately high sampling rate for the given anti-aliasing filter; a digital low pass filter at this higher sample rate; and a resampling of the signal at a lower sample rate that is suitable for general computations. A block diagram for such a scheme is shown in FIG. 2. In this scheme, the sample frequency, ω1, is selected based on the design of the analog anti-aliasing filter, while the sample frequency, ω2, is the desired sampling frequency for the control system.
However, the scheme illustrated in FIG. 2 is often implemented in applications where one set of control and measurement hardware is utilized for multiple applications. Thus, it is not feasible to reconfigure the hardware (e.g., fixed filters) of the system for each different application.